A useful way of exploring how a Major key (like C Major) sounds and feels is to wander around the "Diatonic Cycle of 4ths".
"Diatonic" means "within the key" — so here it means within the key of C Major.
"4ths" means a musical interval of a 4th:
C to F (C - D - E - F) is a diatonic 4th
F to B (F - G - A - B) is a diatonic 4th
B to E (E - F - G - A)is a diatonic 4th
"Cycle" in this case means a repeating pattern of "4ths".
('Cycle of 4ths' is different than a 'Circle of 4ths or 5ths' - those change key centers with almost every move, whereas the Cycle mostly stays in a single key center)
In C Major, we learned the C Major Scale as Letters & Numbers:
Letter Names: C - D - E - F - G - A - B - C
Numbers: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 1
But in this Cycle of 4ths it would re-ordered as:
Letter Names: C - F - B - E - A - D - G - C
Numbers: 1 - 4 - 7 - 3 - 6 - 2 - 5 - 1
WITH 2-3-3
The cycle of 4ths in C Major, using the 2-3-3 format.
WANDERING
This the cycle of 4ths in C Major, wandering around the fretboard (breaking out of the 2-3-3 format.)
Also, the 2-3-3 format is useful for playing modes/scales, but not as user friendly when it come to adding other intervals (i.e. starting to add harmonic language)
ADD A 3RD
The cycle of 4ths in C Major — but with a Diatonic 3rd added above or below each note. We can refer to this 2-note combination as a "Diad".
A "Diad" is 2 notes, as opposed to a "Triad" meaning 3 notes.
A "Diad" is also just an interval (between two pitches), but it can help to think of it as a small chord too!
WANDERING WITH 3RDS
Wandering around the cycle of 4ths in C Major with a Diatonic 3rd added above or below each note.
ADD A 3RD + ADD A 5TH
The cycle of 4ths in C Major Diads — but with an Diatonic 5th added above or below each diad.
A "Triad" meaning 3 notes is commonly considered to be stacked 3rds (i.e. C - E - G, D - F - A, E - G - B, etc.), but you can also think of it as three pitches played together like C - F - G or C - D - G.
WANDERING WITH 3RDS AND 5THS
Wandering around the cycle of 4ths in C Major with a Diatonic 3rd and a Diatonic 5th added above or below each Diad.
On the guitar, 3-note chords are pretty nimble and easy to move around.
SUSPENSIONS
I'm a fan of suspensions. So next we're going to create some simple suspended sounds.
We'll play our Cycle of 4ths, with our 3rds and 5ths like before. But this time we'll hold on to the 5th on some of them:
1 to 4: hold the the 5th of 1, to become the 2nd of 4
7 to 3: hold the the 5th of 7, to become the 2nd of 3
6 to 2: hold the the 5th of 6, to become the 2nd of 2
5 to 1: hold the the 5th of 5, to become the 2nd of 1
SUSPENSIONS TRAIN
We're going to add another set of simple suspensions, so that this exercise wraps around itself:
1 to 4: hold the the 5th of 1, to become the 2nd of 4
7 to 3: hold the the 5th of 7, to become the 2nd of 3
6 to 2: hold the the 5th of 6, to become the 2nd of 2
5 to 1: hold the the 5th of 5, to become the 2nd of 1
4 to 7: hold the the 5th of 4, to become the 2nd of 7
3 to 6: hold the the 5th of 3, to become the 2nd of 6
2 to 5: hold the the 5th of 2, to become the 2nd of 5
...... and around and around we go :)